In the light of the two negative reviews and one comment which all require new analyses and point to fundamental ﬂaws in the methodology of the current paper, I regret to inform you that my conclusion is to support rejection. I strongly dissuade the authors from submitting responses and a revised version.

Let’s talk a little more about the irony of using the Jevrejeva’s 2008 sea level data, which I will refer to as JE08[1], to confirm Rahmstorf’s sea level projections for the 21st century.

As I have already explained, Rahmstorf claims in his 2011 paper (which I will refer to as R2011[2]), that his model is “robust,” meaning that variations of historical 20th century input sea level data yield essentially the same sea level rise projections for the 21st century. R2011 graphically presents seven sources of sea level data (while ignoring others) and implies their similarity by overlaying the same quadratic fit for all of them. R2011 leads us to believe that the model is robust with, specifically, the input of these various sea level data sets.

R2011 presents the results of the model using only three of the seven sea level rise inputs. Two of the three are by the same authors, Church and White[3][4], who clearly believe their later version of the sea level data (CW11[4]) is an improvement over their earlier version (CW06[3]). Then, R2011 cynically rejects the model results from Church’s and White’s better set of data because those results testify against R2011’s desired conclusion of extremely high sea level rises for the 21st century.

Which brings us to Jevrejeva

The third data set that R2011 used is Jevrejeva’s. So after all the blathering about the “robustness” of their model under a broad variety of inputs, R2011 is left with just two sea level data sets that they are satisfied with: Church’s and White’s earlier data set, CW06; and Jevrejeva’s 2008 data, JE08. Figure 1, below shows R2011’s figures 1 and 9, with my annotation.

Keep in mind that R2011’s objective in their claim of robustness was to prove that their earlier results [5], based on the CW06 were realistic. So, in effect, after all the hand waving JE08 is the only one of the seven sea level data sources that fulfills that purpose. That is why we are taking a little closer look at JE08.

Let’s start by looking at an overlay of JE08, CW06 and CW11 in figure 2. If Rahmstorf’s model were “robust,” as R2011 claims, then all three of these data sets as input to the model should yield very similar sea level rise projections for the 21st century. But one of them yields much lower results than the other two. The amazing thing is that the outlier is CW11, which is nearly a twin to CW06, at least compared to JE08. How can that be?

Figure 2

Let’s suspend our higher cognitive functions for the moment and agree with R2011’s reasoning. That is, we will agree that the sea level rise projections for the 21st century based on CW11 input data must be rejected because they are much lower than the projections based on CW06 input data. Inversely, we will agree that sea level rise projections for the 20th century based on JE08 input data must be accepted because they give high 21st century projections, just like the projections based on CW06 input data.

A closer look at JE08 sea level data

Since we have decided to mindlessly accept the usefulness of JE08 to back up Rahmstorf’s high sea level rise projections for the 21st century, then we should also accept some other interesting features of JE08. So let’s take a closer look.

JE08 says their version of sea level data was in “good agreement with estimates of sea level rise during the period 1993–2003 from TOPEX/Poseidon satellite altimeter measurements.” Figure 3, below, shows an overlay JE08 and the satellite altimeter data[6],…

Figure 3

It is quite striking that according to JE08 and the satellite data that the sea level rise rate for the middle third of the 20th century (1933 to 1966) is exactly the same as the sea level rise rate at the end of the 20th century and beginning of the 21st century. How can this possibly be!? How can this data that indicates no increase in the sea level rise rate for 80 years cause tremendous increases in the sea level rise rate for the 21st century when used as input to Rahmstorf’s model?

Stefan the Dart Thrower

Consider Stefan Rahmstorf the Dart Thrower. He holds forth at the pub as the best thrower in the kingdom. He brags about his precision, claiming “I can hit high numbers every time! My talent is robust!” Challenged by another annoyed pub patron to “put up or shut up,” Stefan grabs a handful of darts and goes to work. He throws seven, but only three hit the board. Two are on high numbers and one is on a low number, the rest are stuck in the wall. “See!” he says triumphantly, pointing at the two darts on the high numbers.

The other patron points out the projectiles stuck in the wall. “Bad darts” Stefan replies.

“What about this dart on the low number – it is identical to one of the darts on a high number” the incredulous patron points out. “Same length, same material, same weight, same manufacturer.”

“Obviously a bad dart, nevertheless” sniffs Stefan. “If if were a good dart it would have landed on a high number.”

Recall figure 1 from R2011[1]…

One of the primary points of this graphic is the quadratic fit of one data set (CW06) overlaid on all the other data sets. The message that you are to receive is that these various sets of sea level data all tell the same essential story. The falseness of this claim was discussed in “Quadratic fits of laughter.”

But let’s take Rahmstorf at his word. Let’s agree with him that these sea level data sets all tell essentially the same story. R2011’s big point is that the Rahmstorf model is “robust” given a variety of different historical data sources. So it seems a tad bit strange that after going to all the trouble to point out these various sea level data sources and their similarities, he only gives the projection results of his model for three of them (CW06[2], CW11[3], and JE08[4]).

Of those three input sea level data sets, only two of them give similar sea level projections for the 21st century. The outlier which results from CW11 shows significantly lower sea level projections. Because of this, the outlier must be rejected (according to R2011), even though Church and White, the authors of both CW06 and CW11, clearly think the CW11 data is an improvement over their Cw06 data.

What about some of the other sea level rise data sets shown in R2011’s figure 1? What type of 21st century sea level projections do they yield when inserted into Rahmstorf’s model?

Holgate’s sea level data

Let’s consider the sea level rise data of Simon Holgate. The above image shows Holgate’s 2004 data[5], labeled HW04. As I have previously pointed out, R2011 oddly includes Holgate’s 2004 data but ignores his 2007 data[6], H07. I will consider both. In my previous post I showed the results of Rahmstorf’s model when either CW06 and CW11 are input with six different combinations of reservoir storage and ground water depletion inputs. The following two graphs show the results in the same format using HW04 and H07 (instead of CWo6 and CW11) with the same combination of reservoir storage and ground water depletion inputs. I have kept the horizontal axis scaling the same as in the previous post to highlight the different results when Church and White data is used and when Holgate data is used. Data files with all the specifics of this data are at the bottom of the post.

FIGURE 2. Sea level rise projections for the 21st century based on my implementation of Rahmstorf’s model under the RCP45 emissions scenario (Moss, 2010)[7] for Holgate sea level data coupled with various combinations of reservoir storage and groundwater depletion data inputs.

FIGURE 3. Sea level rise projections for the 21st century based on my implementation of Rahmstorf’s model under the RCP85 emissions scenario (Moss, 2010)[7] for Holgate sea level data coupled with various combinations of reservoir storage and groundwater depletion data inputs.

For comparison, here are the previously posted results using Church and White sea level data…

RCP45

RCP85

Hmmm…

Didn’t R2011 imply that those various sea level data sets shown if figure 1, above, told the same essential story? Yes, I believe he did! That is why they overlaid the same quadratic fit onto all of them.

And didn’t R2011 say that their model was “robust?” Yes, I am quite certain that they did! In fact the word “robust” was in the title of their paper, and they said…

“We determine the parameters of the semiempirical link between global temperature and global sea level in a wide variety of ways…We then compare projections of all these different model versions (over 30) for a moderate global warming scenario for the period 2000–2100. We find the projections are robust“

and

“we will systematically explore how robust semi-empirical sea level projections are with respect to the choice of data sets”

So, they claim to use “a wide variety of ways” to look at “all these different model versions (over 30).” They show plots of seven different sea level data sets and imply their similarity. But they only show projections based on three of them. Then they reject the projections based on one of the three, even though it is arguably the best sea level data of the bunch.

What do they say about their model’s projections based on the “wide variety” other sea level data sets that look so good overlaid with the same quadratic fit…?

Cricket. Cricket.

How would R2011 reject the projections based on the Holgate data?

How would R2011 reject the projections based on the Holgate data that I have shown above in figures 2 and 3? Well they would undoubtedly point out that the fit parameter, To (the so called baseline temperature, is way too low. Recall, R2011 finds To to be on the order of -0.4 °C (below the 1950 to 1980 global average). When Holgate’s sea level data is used, To is on the order of -4.0 °C. Hey Rahmstorf, don’t blame me, its your model!

Maybe one of these days I will write a justification for a large negative To. It is really quite simple. But I am going to conclude for today.

Which of the many projections do I endorse?

Which projections are better – the ones based on CW06, CW11, JE08, HW04, or H07? None of them. As I have pointed out over and over, the Rahmstorf model is bogus, bogus, bogus. I have now shown, again, that it is also not robust. It is only marginally better than a random number generator. HIgher temperatures would likely lead to higher sea levels, but Rahmstorf’s model is useless in determining how much.

Data files with specifics of of my implementation of Rahmstorf’s model using Holgate sea level data

I will refer to Stefan Rahmstorf’s ”Testing the robustness of semi-empirical sea level projections” as R2011 [1].

What does R2011 mean by “robust?”

What does Rahmstorf mean when he says his model linking sea level to temperature is “robust?” Simply this: when the inputs that he deems acceptable are inserted into his model, he gets the results he likes.

How does he decide which inputs are acceptable? Easy – if they yield the results he likes, then they are acceptable. It is a very simple and efficient system of logic!

Why a paper about “robustness?”

Rahmstorf and his associates have a pressing need to defend their sea level rise projections. I have presented a host of reasons why his model is bogus. One of the most embarrassing is that one of his fit parameters, that he expected to be positive, is in fact negative for every combination of input tried. This leads to all kinds of bizarre results (see here, here and here , for example). The other is that his sea level projections dropped dramatically when his preferred source of 20th century historical input data updated their data set.

This “robustness” paper (R2011) is a stumbling attempt to dismiss the revised sea level data from the source that he had previously enthusiastically used.

A quick recap

Rahmstorf’s model, which I will refer to as the VR2009[2] model, attempts to relate global sea level rise to global temperature through the following formula…

where H is sea level and T is temperature. Insert historical data for H and T, and solve to a, b, and To. Then insert projected temperatures for the 21st century and calculate projected sea level rises for the 21st century. The VR2009 model and approach have an amazing number of problems and the list just keeps getting longer. There is a whole family of realistic temperature scenarios for the 21st century that cause this model to yield ridiculous results (see here). The root of most of these problems comes from the fact that every set of historical sea level inputs and temperatures that Rahmstorf and associates have tried result in a negative b. That includes every set of input data considered in R2011 (see figure 1, below).

Model inputs and projections in R2011

(click to enlarge) …

I have circled the results R2011 likes. As you can see, nothing involving the Church’s and White’s 2011 sea level data (CW11)[4] meets R2011’s quality standard. R2011 has determined that Church’s and White’s 2006 sea level data (CW06)[5] is better than Church’s and White’s 2011 data, despite the fact that Church and White obviously think their updated 2011 data is better.

It comes down to To

Why does R2011 think the 2006 sea level data is better than the improved 2011 sea level data? Well, I have already explained that – the 2006 Church and White sea level data gives the results that R2011 wants – higher sea level rise projections for the 21st century!

But they can’t really say that. Instead they say that the 2011 Church and White data leads to a baseline temperature, To, that they insist is too low. To is the steady-state temperature deviation from the 1950-1980 average temperature at which Rahmstorf’s model says the sea level would be unchanging.

Look at the right side of figure 1. It shows the baseline temperature that R2011 derived with the various sets of input data. The values of To that meet with R2011’s approval average out to about -0.43 degrees. But those based on CW11 average out to about -0.62 degrees C. A difference of less than two tenths of a degree.

If you were to ask the authors of R2011 what other evidence do they have that To must be about -0.43 degrees, they will refer you to “Climate related sea-level variations over the past two millennia[6],” which used evidence from two salt marshes in North Carolina to corroborate this global value. And they have great confidence in this independent confirmation (because two out of three of the R2011 authors were also authors on this paper). Hmmm.

I will have more to say about R2011’s preference for To in a later post.

A few input combinations that R2011 did not show you

R2011 implies that it has tried some vast universe of input sea level and temperature data combinations in their model. They say “We then compare projections of all these different model versions (over 30)…” Wow! Count them – over 30!

But there are many more possible combinations than that. R2011 has picked a few cherries from a very prolific tree.

In figures 2 and 3, below, I have run several temperature and sea level input data sets in my implementation of Rahmstorf’s model. In some cases my input combinations are the same as some found in figure 1. In some cases they are different. I have arranged the input combinations in chronological order, with older versions of input data on the bottom. Notice a trend? Figure 2 and figure 3 give projections based on the RCP45 and RCP85 emission scenarios, respectively.

FIGURE 2. Sea level rise projections for the 21st century based on my implementation of Rahmstorf’s model under the RCP45 emissions scenario (Moss, 2010) for various temperature and sea level input data sets.

FIGURE 3. Sea level rise projections for the 21st century based on my implementation of Rahmstorf’s model under the RCP85 emissions scenario (Moss, 2010) for various temperature and sea level input data sets.

As you can see, newer sea level data (whether it is actually sea level (CW06 vs CH11, or reservoir storage (RS) or ground water depletion (GWD) modifiers) tends to lead to lower 21st century projections when inserted into Rahmstorf’s model.

Which projection do I endorse? None of them. Make no mistake – the Rahmstorf model is bogus, no matter what the inputs are. I am just playing games with it. The Rahmstorf model is an illusion that hooks you with a simple truth: It is a pretty good bet that higher temperatures lead to higher sea levels. But the Rahmstorf model is not much better than a Ouija board for quantifying how much.

There is much to be said about the results in figures 2 and 3. The 48 files below give the long story that is summarized in figures 2 and 3.

I will refer to Stefan Rahmstorf’s ”Testing the robustness of semi-empirical sea level projections” as R2011 [1].

The new code for consistent processing of temperature and sea level data according to the predominant Vermeer and Rahmstorf 2009 model (VR2009)[2] is complete.

It is written LabView V7.1. There have been several upgrades to LabView since V7.1, but I believe my code will open in any of them. I prefer this older version of LabView for a variety of reasons that I will not go into here. But one advantage is that anyone who is interested in running this code can find a used student version of LabView on Ebay at a very reasonable cost.

Rahmstorf and company figured that once a, b, and To were found they could insert hypothesized temperature scenarios for the 21st century into equation 1 and calculate the resulting sea levels. I have provided a long list of criticisms of their logic. One of the most devastating observations is that their own source of 20th century sea level data(Church and White, 2006[3]) had revised their data, and the new version of data (Church and White 2009[4] or Church and White 2011[5]) resulted in much lower sea levels by the end of the 21st century when inserted in to equation 1.

In R2011 Rahmstorf re-works the numbers with the same inputs used in VR2009, and I have reworked the numbers with this new code. And for the same inputs used back on VR2009, everything lines up within Rahmstorf’s stated uncertainties. But that is a minor point. Rahmstorf’s primary objective in R2011 is to defuse my observation that Church’s and White’s newer, more accurate sea level data causes Rahmstorf’s model to yield much lower sea level projections for the 21st century. Plenty of time to deal with that issue later.

But for now and for the record: in VR2009 Vermeer and Rahmstorf found

a = 5.6 ± 0.5 mm/year/K

b= -49 ± 10 mm/K

To = -0.41 ± 0.03 K

In 2010, using my implementation of their model, I found

a = 5.6 mm/year/K

b= -52 mm/K

To = -0.42 K

In R2011 Rahmstorf presents slightly different numbers than he did in VR2009 for the same input conditions. Similarly, with my new code I now get slightly different numbers for the same input conditions.

With the new code I found

a = 5.8 mm/year/K

b= -54 mm/K

To = -0.41 K

Presentation of my results

In R2011 Rahmstorf makes some claims based the same model as equation 1, but with various combinations of temperature and sea level data from different sources. His claim is that he gets essentially the same results – no matter what inputs he uses – indicting that his model is “robust.”

I will also be presenting a lot of results for different possible inputs in the days to come. But my results will be very detailed, complete, and entirely open for your examination. You also have access to my complete code.

My code will always generate four files for any set of inputs. Three of those files are images of: graphs of the input data; graphs of the model fits to the input data (used to derive a, b, and To); and graphs of sea level projections based on various temperature scenarios for the 21st century, including the SRES emission scenarios used in VR2009 and the RCP45 and RCP85 scenarios used in R2011. The fourth file is a tab delimited text file with all setup parameters, fit plots and results, and projections.

Note that the graph images of the 21st century sea level projections will not be autoscaled. That is, the Y axis of the projection graphs will all have the same scaling. This will make many of the graphs look crowded, but it will also be easy to make a qualitative comparison of the projections from different input data. You can always open the tab delimited text file in the spreadsheet of your choice and replot the data as you see fit.

Below you can see an example of the graph images and the corresponding tab delimited text file that is generated by my code with the same input data used to find the model fit parameters listed above. That is, I will use the GISS temperature, Church and White’s 2006 sea level data and the Chao reservoir correction, which result in my values of a, b, and To, shown above.

The tab delimited text file is shown below. I have truncated the columns of data (which could be thousands of rows long). The headers and columns would line up better if you opened the file in a spreadsheet.

I have finally published my small library of temperature, sea-level and sea-level modifier (reservoir storage, groundwater depletion, etc.) data from various sources.

All of these data files have a consistent format which can be read by my code that calculates fit parameters for the Rahmstorf model relating sea level to temperature. However, not all of the time series are long enough to be useful in that model.

I am open to suggestions for additions to this list. If you have any criticisms of the files, such as accuracy of the data, format, selection, anything – please leave a comment. I will give due attention to any legitimate criticism that is aimed at improving the data.

Coming soon…

I am a slow worker, but I try to be thorough.

The first output from my code, using Rahmstorf’s preferred inputs (GISS temperature, Church and White 2006 sea level data, and the Chao reservoir correction) will be presented soon. The goal of that presentation will be two-fold: to verify that of my model implementation are consistent with Rahmstorfs; to have a simple format for presenting those result. That format can then be applied to the results of other input data.

I have seen something in R2011 that I have never seen before. The use of a quadratic fit as a kind of “optical delusion.”

Consider the image at the right. Do you see the triangle? Sure you do. Of course, it is not really there. But what would you say if I insisted that the triangle really was there and said “The circles are shown merely to help the eye find the triangle?”

R2011 has done much the same thing with a quadratic data fit in their figure 1. I would think what they have done was just a joke, if it weren’t such an obvious attempt to convince readers that the data says something that it does not say. Take a look…

Note the dashed grey lines through each data set. As R2011 explains in their caption, these dashed grey lines which pass through all the data sets, are actually the quadratic fit to just one of the data sets (CW06)[2]. They say

“The dashed grey line is a quadratic fit to the CW06 data, shown here merely to help the eye in the comparison of the data sets.”

The point the R2011 wants to make, of course, is that all of these data sets have the same acceleration trend as R2011’s preferred sea level data, CW06.

But that is not true. In fact, if you fit any of the other data sets to a quadratic you will see that every single one of them has a lower trend than CW06 when projected through the 21st century. Every single one of them.

The following figure shows proper quadratic fits to all the sea level data sets used by R2011 in their figure 1. The legend shows the sea level rise that would result for the period 2000 to 2100 if these quadratics were extrapolated to 2100.

Quadratic fits for all sea level data sets used by R2011 in their figure 1. The legend shows the sea level rise that would result for the period 2000 to 2100 if these quadratics were extrapolated to 2100

Updated Holgate data

Science is about constant refinement of theories and data. When Rahmstorf is faced with old data and new data from the same authors, he has a special method for deciding which data set is better. The version that points to higher sea level rise in the 21st century is always considered to be better. Thus his insistence that the 2006 Chuch and White sea level data is better than the 2009 or 2011 Church and White data that incorporated Church’s and White’s data reduction improvements.

The same is true for Holgate’s sea level data. Look at HW04 [3] plots in the above graphs. This Holgate sea level data covers the mid-1950s to the mid-1990s. It is a curious thing (not really curious if you understand Rahmstorf’s modus operandi) that R2011 chose this data over Holgate’s updated data from 2007 [4], which covers the entire 20th century. What would happen if we replaced the HW04 data with the 2007 Holgate data (H07)? Take a look…

Holgate data from 2004 has been replaces with Holgates updated data from 2007.

Let me stress again, I do not recommend extrapolating sea level data with quadratic fit, and I am not endorsing any of the extrapolations shown above. I am simply guffawing at Rahmstorf’s chuzpa in his figure 1.